Miguel is designing shipping boxes that are rectangular prisms. The shape of one box, with height h in feet, has a volume defined by the function V(h) = h(h – 10)(h – 8). Graph the function. What is the maximum volume for the domain 0

Question

Miguel is designing shipping boxes that are rectangular prisms. The shape of one box, with height h in feet, has a volume defined by the function V(h) = h(h – 10)(h – 8). Graph the function. What is the maximum volume for the domain 0 < h < 10? Round to the nearest cubic foot.

anonymous · Answer

@jim_thompson5910 
@zepdrix

anonymous · Answer

http://www.calculusapplets.com/boxproblem.html hope this helps, i cant remember how to do this

zepdrix · Answer

If we look at the Volume function, we can try to graph it based on what we KNOW about a cubic function, and the information they gave us about it's roots.

The roots are where it crosses the x-axis, or in this case the h-axis.
They gave us the function nice and factored already so we can easily determine that this function has roots h=0, h=8 and h=10.

Graphing the function should give us something like this,|dw:1356737814476:dw|